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\begin{document}

\title{DFT calculation of the Renner Teller Effect in NCO: Preliminary
assessment of Exact Exchange Energy on the accuracy of the
X\textsuperscript{2}\selectlanguage{greek}Π \selectlanguage{english}Renner Coefficient\selectlanguage{english}}



\author[1]{David Kashinski}%
\author[1]{Tyler Radziewicz}%
\author[1]{Matthew Suarez}%
\author[1]{Constantine Stephens}%
\author[2]{Edward Byrd}%
\affil[1]{United States Military Academy at West Point}%
\affil[2]{Army Research Laboratory Aberdeen Proving Ground}%


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  \date{May 16, 2024}


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\begin{abstract}
Assessment of DFT methods through analysis of the Renner-Teller Effect
(RTE) in the X\textsuperscript{2}\selectlanguage{greek}Π \selectlanguage{english}state of the NCO radical was
completed. Our results suggest that the amount of exact exchange at long
range is important for an accurate description of the RTE in NCO. DFT
functionals from the B3LYP, PBE, TPSS, M06, and M11 families with
standard Correlation Consistent, 6-311G split valence family, as well as
Sadlej, and Sapporo polarized triple-\selectlanguage{greek}ζ \selectlanguage{english}basis sets were assessed. Our
Renner coefficients are compared with previously published theoretical
and experimental results to characterize the overall accuracy of various
functional/basis set combinations in determining the RTE splitting in
the \selectlanguage{greek}Π \selectlanguage{english}(bending) modes of NCO(X\textsuperscript{2}\selectlanguage{greek}Π\selectlanguage{english}). We suggest that
this method of analysis can be extended to other systems, serve as an
accuracy metric when selecting a functional, and provide a means to
create training sets for machine learning in computational molecular
physics applications.%
\end{abstract}%



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